Microsoft Word - Digital Logic Design v_4_6a

Digital Logic Design Version 4.6 printed on February 2016 First published on August 2006 ...

Background and Acknowledgements This material has been developed for the first course in Digital Logic Design. The content is de ...

Contents ...

...

Chapter 1. Number Systems, Number Representations, and Codes 1.1. Key concepts and Overview 1.2. Digital vs. Analog 1.3. Digita ...

Chapter 1. Number Systems, Number Representations, and Codes 1.1. Key concepts and Overview  Digital vs. Analog  Digital Desig ...

1.2. Digital vs. Analog Natural forces and signals are all analog (or continuous) which means we hear, see and change items in a ...

 Example of analog and digital representations of human Heart Beat:  Based on the definition of a digital (2-valued) system, w ...

1.3. Digital Design Overview (from Transistor to Super Computer)  All digital systems from the smallest to largest run on a 2-v ...

Medium Scale Integration, MSI  PAL--Programmable Array Logic, GAL--Generic Array Logic, EPROM--Erasable Programmable Read Onl ...

1.4. Design Methodologies Digital design depends on the type of problem, the work already completed, the strategic direction of ...

1.5. Number Systems (Decimal, Binary, Octal, Hexadecimal) We have learned and use the decimal numbering system simply because hu ...

(1010.11) 2 = 8 + 0 + 2 + 0 + 0.5 + 0.25 = (10.75) 10 Note: The general term for decimal point is radix point
In binary, the c ...

1.6. Base Conversions  Decimal to Binary Conversion
Alternative 1 – “Subtract the weight method”  Steps: ♦ Find the largest ...

Step: (1) Each three bits in binary (right to left) equals one octal digit in the same direction)
Example - Convert (1011011 ...

 Example: Convert (52) 10 to binary (radix, r = 2) Therefore (52) 10 = (110100) 2  Decimal Fraction Conversion to any Base – “ ...

1.7. Signed Binary Number Conventions  Signed Binary Number Representations (3 methods)
Signed Magnitude (SM)  Easiest for p ...

Here is an example of 4-bit word size:
DRC numbers for n-bit word ranges from +(2n-1 – 1) to –(2 n-1 – 1)  Note that there ...

RC numbers for n-bit word range from +(2 n-1 – 1) to –(2 n-1) with the following two characteristics:  The range is not symme ...

1.8. Binary Arithmetic All of today’s computer systems use RC numbers (2’s complement) for binary arithmetic operations. The res ...